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A332228
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Odd numbers n, not powers of primes, such that sigma(n) is congruent to 2 modulo 8.
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6
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153, 325, 369, 657, 725, 801, 833, 845, 873, 925, 1017, 1233, 1325, 1377, 1445, 1525, 1737, 2009, 2057, 2097, 2169, 2313, 2525, 2529, 2725, 2817, 2925, 3033, 3177, 3321, 3577, 3609, 3681, 3725, 3757, 3897, 3925, 4041, 4113, 4205, 4325, 4361, 4525, 4689, 4753, 4901, 4925, 4961, 5121, 5193, 5337, 5409, 5537, 5553, 5725
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OFFSET
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1,1
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COMMENTS
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Proof that any odd perfect number, if such numbers exist at all, has to reside in this sequence: As all terms in A228058 are = 1 modulo 4 (their binary expansion ends as "01"), and taking sigma of an odd perfect number would multiply it by two (shift one bit-position left), the base-2 expansion of that result would end as "010"), i.e., sigma(k) modulo 8 should be 2 (not 6) for such numbers k.
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LINKS
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PROG
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(PARI) isA332228(n) = ((n%2)&&!isprimepower(n)&&2==(sigma(n)%8));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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